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    <title>htrianr</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>htrianr</b> -  triangularization of polynomial matrix</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[Ar,U,rk]=htrianr(A)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>A</b>
        </tt>: polynomial matrix</li>
      <li>
        <tt>
          <b>Ar</b>
        </tt>: polynomial matrix</li>
      <li>
        <tt>
          <b>U</b>
        </tt>: unimodular polynomial matrix</li>
      <li>
        <tt>
          <b>rk</b>
        </tt>: integer, normal rank of <tt>
          <b>A</b>
        </tt>
      </li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    triangularization of polynomial matrix <tt>
        <b>A</b>
      </tt>.</p>
    <p>
      <tt>
        <b>A</b>
      </tt> is <tt>
        <b>[m,n]</b>
      </tt> ,   <tt>
        <b>m &lt;= n</b>
      </tt>.</p>
    <p>
      <tt>
        <b>Ar=A*U</b>
      </tt>
    </p>
    <p>
    Warning: there is an elimination of "small" terms (see function code).</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

x=poly(0,'x');
M=[x;x^2;2+x^3]*[1,x-2,x^4];
[Mu,U,rk]=htrianr(M)
det(U)
M*U(:,1:2)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="hrmt.htm">
        <tt>
          <b>hrmt</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="colcompr.htm">
        <tt>
          <b>colcompr</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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